What is Case:Calculate Mean when Frequencies are not Given

Example: A market with 168 operating firms has the following distribution of average number of workers in various income groups:

Income groups :

150—300

300—500

500—800

800—1200

1200—1800

No. of firms :

40

32

26

28

42

Average No. :

of workers :

8

12

7.5

8.5

Find the average salary paid in the whole market.

Solution

In this question frequencies are not given. The frequencies can be obtained by multiplying the number of firms with the average number of workers:— Computation of Average Salary Paid

Income-groupX(1)

Mid-valuem(m.v.) (2)

No. offirms(3)

Average No. ofWorkers(4)

frequency(f)(3x4) (5)

mf(2x5) (6)

150-300

225

40

8

320

72,006

300-500

400

32

12

384

1,53,600

500-800

650

26

7.5

195

1,26,750

800-1,200

1,000

28

8.5

238

2,38,000

1,200-1,800

1,500

42

4

168

2,52,000

N=1,305

∑mf=8,42,350

Mean = X = ∑mf / N = 8,42,350 / 1305 = 645.4789 $

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